Question

Question 56 After living in a university residence for one year, Jane decides to rent an apartment for the remaining three years of her degree. She has found a nice location that will cost $555 per month. Rent for the first and last month must be paid up front. How much money would Jane need to have in her bank account right now to be sure she will always have enough for rent? The bank account pays 9.6 percent interest, compounded monthly. (Round answer to 2 decimal places, e.g. 125.12. Do not round your intermediate calculations.) Amount Jane would need to have right now 17574.13

Answer 1

Monthly Rent = $555

Rent to be Paid for no of months = 3 years*12 months = 36

As, First and last month rent is required upfront, we will calculate the present Value of these payments made at the end of 2 months till 35 th payment.

Present Value = C*[1-(1+r)^-n]/r

Where, C= Periodic Payments = $555

r = Periodic Interest rate = 0.096/12 = 0.008

n= no of periods = 34 (From 2nd to 35th)

Present Value = 555*[1-(1+0.008)^-34]/0.08

Present Value = 555*[1-0.76267921]/0.08

Present Value = $ 16,464.13

Total Money needed today = Value today + Upfront payments

= $ 16464.13 + ($555 + $555)

= $ 17574.13

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